

A163799


a(n) is the nth J_19prime (Josephus_19 prime).


2



15, 145, 149, 243, 259, 449, 1921, 2787, 15871, 18563, 26459, 191515, 283269, 741343, 844805
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OFFSET

1,1


COMMENTS

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 19th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_19prime if this permutation consists of a single cycle of length N.
There are 15 J_19primes in the interval 2..1000000 only. No formula is known; the J_19primes have been found by exhaustive search.


REFERENCES

R. L. Graham, D. E. Knuth & O. Patashnik, Concrete Mathematics (1989), AddisonWesley, Reading, MA. Sections 1.3 & 3.3.


LINKS

Table of n, a(n) for n=1..15.
P. R. J. Asveld, Permuting Operations on Strings and Their Relation to Prime Numbers, Discrete Applied Mathematics 159 (2011) 19151932.
P. R. J. Asveld, Permuting Operations on StringsTheir Permutations and Their Primes, Twente University of Technology, 2014. University link.
Index entries for sequences related to the Josephus Problem


EXAMPLE

All J_19primes are odd.


CROSSREFS

Cf. A163762 through A163798 and A163800 for J_2 through J_18 and J_20primes.
Sequence in context: A243418 A270511 A026893 * A206810 A025440 A155638
Adjacent sequences: A163796 A163797 A163798 * A163800 A163801 A163802


KEYWORD

nonn,more


AUTHOR

Peter R. J. Asveld, Aug 04 2009


STATUS

approved



